AAPL wrote:GMAT Prep

The numbers x and y are NOT integers. The value of x is closest to which integer?

(1) 4 is the integer that is closest to x+y
(2) 1 is the integer that is closest to x-y

OA E

Target question: The value of x is closest to which integer?

Let's head straight to...........

Statements 1 and 2 combined
There are several values of x and y that satisfy BOTH statements. Here are two:
Case a: x = 2.4 and y = 1.4. These values satisfy both statements. In this case, the answer to the target question is 2 is the closest integer to x
Case b: x = 2.6 and y = 1.4. These values satisfy both statements. In this case, the answer to the target question is 3 is the closest integer to x
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

AAPL wrote:GMAT Prep

The numbers x and y are NOT integers. The value of x is closest to which integer?

(1) 4 is the integer that is closest to x + y
(2) 1 is the integer that is closest to x - y

OA E

Let's take each statement one by one.

(1) 4 is the integer that is closest to x + y.

=> 4.5 > x + y ≥ 3.5

We do not have any information about y. Insufficient.

(2) 1 is the integer that is closest to x - y.

=> 1.5 > x - y ≥ 0.5

We do not have any information about y. Insufficient.

(1) and (2) together

We have

4.5 > x + y ≥ 3.5 ---(1) and
1.5 > x - y ≥ 0.5 ---(2)

Adding (1) and (2), we have

6 > 2x ≥ 4
3 > x ≥ 2

If, say x = 2.1, the integer closed to x is 2; however, if, say x = 2.8, the integer closed to x is 3. No unique value. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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